|Covid-19|March 8 – The Province of Carolina incorporates the town of Bath, making it the first incorporated town in present day North Carolina. The town becomes the political center and de facto capital of the northern portion of the Province of Carolina until Edenton is incorporated in 1722.
April 16 – Anne, Queen of Great Britain honours Isaac Newton with a Knight Bachelor
May – The Twelfth Siege of Gibraltar ends with the defending Confederate forces retaining control of the town.
May 5 – Joseph I, Holy Roman Emperor succeeds his father Leopold I.
November – In Williamsburg, capital of the Virginia colony in America, construction of the Capitol building is completed.
November 5 – The Dublin Gazette publishes its first edition.
November 15 – The Battle of Zsibó - the Austrian-Danish forces defeated the Kurucs (Hungarians)
December – The Sophia Naturalization Act is passed by the English Parliament, which naturalizes Sophia of Hanover and the "issue of her body" as English subjects.
December 25 – In Munich, capital of Bavaria, 1,100 militiamen from the Oberland are killed during the Sendlinger Mordweihnacht, after a failed attempt to break through several gates and capture a depot to seize better weaponry; many men were slaughtered by German federal infantry and Hungarian Husars, despite their capitulation to Austrian officers.
Construction begins on Blenheim Palace, in Oxfordshire, England. It is completed in 1724.
Taichung City, Taiwan is founded as the village of Dadun.
With the interest paid from daimyō loans, the Konoike buy a tract of ponds and swampland, turn the land into rice paddies and settle 480 households numbering perhaps 2,880 peasants on the land.
The Shogunate confiscates the property of a merchant in Osaka "for conduct unbecoming a member of the commercial class". The government seizes 50 pairs of gold screens, 360 carpets, several mansions, 48 granaries and warehouses scattered around the country and hundreds of thousands of gold pieces.
January 14 – Jean-Baptiste Charles Bouvet de Lozier, French governor of the Mascarene Islands (d. 1786)
January 24 – Farinelli, Italian castrato (d. 1782)
February 15 – Charles-André van Loo, French painter (d. 1765)
February 21 – Edward Hawke, 1st Baron Hawke, British naval officer (d. 1781)
February 22 – Peter Artedi, Swedish naturalist (d. 1735)
March 2 – William Murray, 1st Earl of Mansfield, Scottish judge and politician (d. 1793)
April 11 – William Cookworthy, English chemist (d. 1780)
July 23 – Francis Blomefield, English topographer (d. 1752)
August 8 – Gustaaf Willem van Imhoff, Dutch Governor-General of the Dutch East Indies (d. 1750)
August 30 – David Hartley, English philosopher (d. 1757)
September 24 – Leopold Josef Graf Daun, Austrian field marshal (d. 1766)
September 28 – Henry Fox, 1st Baron Holland, English statesman (d. 1774)
October 23 – Maximilian Ulysses Count Browne, Austrian field marshal (d. 1757)
October 31 – Pope Clement XIV (d. 1774)
November 23 – Thomas Birch, British historian (d. 1766)
date unknown – Dick Turpin, English highwayman (d. 1739)
date unknown – Faustina Pignatelli, Italian mathematician (b. 1785)
January 12 – Luca Giordano, Italian artist (b. 1634)
January 17 – John Ray, English naturalist (b. 1627)
February 5 – Philipp Jakob Spener, German theologian (b. 1653)
May 5 – Leopold I, Holy Roman Emperor (b. 1640)
July 12 (or 13) – Titus Oates, English conspirator (b. 1648)
August 16 – Jacob Bernoulli, Swiss mathematician (b. 1654)
October 11 – Guillaume Amontons, French physicist and instrument maker (b. 1663)
November 10 – Justine Siegemund, German midwife (born 1636)
November 30 – Catherine of Braganza, queen of Charles II of England (b. 1638)
date unknown – Meg Shelton, alleged witch from Lancashire
1705 (MDCCV) was a common year starting on Thursday (dominical letter D) of the Gregorian calendar and a common year starting on Monday (dominical letter G) of the Julian calendar, the 1705th year of the Common Era (CE) and Anno Domini (AD) designations, the 705th year of the 2nd millennium, the 5th year of the 18th century, and the 6th year of the 1700s decade. As of the start of 1705, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923. In the Swedish calendar it was a common year starting on Sunday, one day ahead of the Julian and ten days behind the Gregorian calendar.